Matty Cohen's injury time strike booked the Potters passage into the last 32 of the FA Youth Cup.
In an entertaining game the Potters and Carlisle struggled to put the ball in the net and it was left to centre back Cohem to decide the tie with virtually the last kick of the game.
Stoke looked dangerous thorughout, Louis Moult somehow not finding the net as he struck the woodwork and forced the keeper into numerous saves whilst Carlisle's 19 goal striker Ryan Bowman was denied by an outstanding save from keeper David Parton.
The Potters return from Brunton Park with a place in Fridays fourth round draw and will be hoping to go far in this seasons competition.